Will I need to buy a new television set to receive DTT?

NO, most current analogue television sets will be able to receive DTT. The main consideration is that your TV must have an A/V input to ensure your Set-Top-Box can be plugged into your TV. If you have this, you should be able to use your current TV set. You do not need a high definition (HF) TV, LCD TV or Plasma TV to receive DTT.
In the next few years, there could also be TVs with an integrated Set-Top Box (that means a Set-Top Box already built in with the TV). These are usually called idTVs. However, these are not likely to be available in SA for a long time.